The purpose of this lab is to use linear regression and data analysis to calculate the elasticity constant for a single spring, and for springs arranged in series and in parallel.

Equipment

two springs

slotted masses

mass hanger

meter stick

support stand

Procedure and Data Tables

Part I: Single springs. Complete ten trials for each spring. Initially record the equilibrium length of the spring without any suspended masses.

Then increase the hanging mass by increments of 100 grams and record each stretched length.

Continue until you have suspended a total of 1000 grams from each spring. Remember that the pan contributes 50 grams to each combination. Complete the following data table for each individual spring.

single spring #1
your group's spring

Equilibrium length

_____________

Trial

Total Hanging Mass

Total force (mg)

Final Length

Displacement

1

100 g

2

200 g

3

300 g

4

400 g

5

500 g

6

600 g

7

700 g

8

800 g

9

900 g

10

1000 g

single spring #2
your partnering group's spring

Equilibrium length

_____________

Trial

Total Hanging Mass

Total force (mg)

Final Length

Displacement

1

100 g

2

200 g

3

300 g

4

400 g

5

500 g

6

600 g

7

700 g

8

800 g

9

900 g

10

1000 g

Part II: Springs in Series. Complete five trials using the springs from both groups. Arrange in series by linking them together one below the other. Initially record the equilibrium length of the springs without any suspended masses. Let your trials range from 100 grams to 500 grams.

springs in series

Equilibrium length

_____________

Trial

Total Hanging Mass

Total force (mg)

Final Length

Displacement

1

100 g

2

200 g

3

300 g

4

400 g

5

500 g

Part III: Springs in Parallel. Complete five trials using the srping from both groups arranged side-by-side, or in parallel. Initially record the equilibrium length of the springs without any suspended masses. Let your trials range from 200 grams to 1000 grams. Be careful to make sure that the suspended masses are centered so that they are supported equally by both springs.

springs in parallel

Equilibrium length

_____________

Trial

Total Hanging Mass

Total force (mg)

Final Length

Displacement

1

200 g

2

400 g

3

600 g

4

800 g

5

1000 g

Data Analysis

EXCEL will now graph your data. Minimize your browser, double click My Computer, double click the shared drive and open the file called 1-HookesLawAPC.xls. You will most likely be asked to open the file as "read only" - that is fine. As soon as the file is open, use File Save As to rename the file as

LastnameLastnameHookesLaw.xls

on the shared drive. This copy of the file now belongs uniquely to your group. Remember that there are to be no spaces in the file name.

What is the name of your file?

Once you save your file with all of the information for each of the individual springs as well as the two special arrangements, go back and rescale any axes to insure that you maximize the display of your data. Then obtain a printout.

What is the numerical value of the slope of the individual graph of spring #1?

Write the equation of your group's graph using the correct experimental variables instead of EXCEL's generic x and y?

What is the numerical value of the slope of your partnering team's graph of spring #2?

Hooke's Law

When working with springs, Hooke's Law states that
Fdistorting = ks
where
Fdistorting is the applied force, k is the spring's elasticity constant measured in N/m, and s is the displacement, or how far the spring is stretched from its equilibrium position.

ALERT! Note that in our lab our graphs have the applied force (the suspended weights) displayed on the x-axis and the spring displacements along the y-axis. This is because we manipulated the values of the suspended masses, resulting in force or weight being our independent variable while we merely recorded the stretched lengths as our experimental outcomes, or dependent values.

Consequently our graphs are titled Displacement vs Force and the elasticity constant for each of our spring systems will be calculated as the reciprocal of each graph's slope.

What is the elasticity constant for your group's original spring?

What is the elasticity constant for your partnering group's spring?

Springs in Series

We will now investigate the elasticity constant for springs arranged in series. The theoretical constant for such a system of springs is given by the formula:

What is the slope of your third graph when your springs were arranged in series?

Based on this slope, what is your experimental elasticity constant for when your springs were arranged in series?

Based on the formula, what is the theoretical value for the elasticity constant when your springs were arranged in series? (Show your calculations next to this graph.)

What is your percent error for this phase of the experiment? (Show your calculations next to this graph.)

How much energy was stored in the spring system when it supported 400 grams?

Springs in Parallel

We will now investigate the elasticity constant for springs arranged in parallel. The theoretical constant for a system of springs in parallel is given by the formula:

What is the slope of your fourth graph when your springs were arranged in parallel?

Based on this slope, what is the experimental elasticity constant for when your springs were arranged in parallel?

Based on the formula, what is the theoretical values for the elasticity constant when your springs were arranged in parallel? (Show your calculations next to this graph.)

What is your percent error for this phase of the experiment? (Show your calculations next to this graph.)

How much energy was stored in the spring system when it supported 400 grams?

Summary

When springs are connected in series, the spring constant of the system ____ when compared with the elasticity constant for either of the original springs:

increaseddecreasedremained the same

When springs are connected in parallel, the spring constant of the system ____ when compared with the elasticity constant for either of the original springs:

increaseddecreasedremained the same

Which arrangement of springs resulted in the greater amount of energy being stored in the system when syupporting 400 grams?

parallelseriesthe same

After submitting your results online, turn in your written lab report to the one-way box. Each group should have a paper to support any and all numerical values that were submitted online as well as a printout of your graphs.